Question

THIS QUESTION IS EASY, I JUST NEED EXPLANATION.

If x is a positive integer, which expression is equivalent to 4 sqrt x^3/5 sqrt x^2 ?
Assume x>0.

Answer 1

It would help to have the question. But I'll guess

`\sqrt[4]{x^(\frac 3 5)}{√(x^2)} = ((x^(\frac 3 5))^(\frac 1 4)) }{ x} = x^{\frac 3{20}} x = x \sqrt[20]{x^3}`

2nd choice.

I forgot the explanation because I was so glad to have puzzled out the question.

The fourth root is the same as the 1/4 th power.

If we know x is positive
`√(x^2)=|x|=x`


`\sqrt[4]{x^(\frac 3 5)}{√(x^2)}`


`= ((x^(\frac 3 5))^(\frac 1 4)) }{ x}`

We multiply the powers:
`(a^b)^c=a^(bc)`


`= x^{\frac 3{20}} x`

The one-twentieth power is the twentieth root. We bring the additional factor of x to the front.


`= x \sqrt[20]{x^3}`

Answer 2

Answer:the answer is A. ^20 sqrt x^7

Explanation:

Just took the test